Reading the notation

A small set of symbols carries every part of this paper — get them precise, since mixing up a function and its derivative is the single most common way marks are lost.

📖 Symbols used in calculus methods

7 terms

Cover the right column and check you can say what each one means.

f(x), y: The function itself — a rule that gives a y-value for every x-value.
f'(x), dy/dx: The DERIVATIVE — the gradient function. Gives the gradient of f(x) at any x-value.
Turning point: A point where f'(x) = 0 — the curve is momentarily flat.
Local maximum / minimum: A turning point where the gradient changes + to − (max) or − to + (min).
f''(x): The second derivative — differentiate f'(x) again. Negative at a turning point ⇒ maximum; positive ⇒ minimum.
+c: The constant of integration — lost whenever you differentiate, so it must be recovered from a given point when you integrate back.
Definite integral: The signed area between a curve and the x-axis over a stated interval — top boundary value minus bottom boundary value.

Practice for this standard covers the whole topic — flashcards and quiz.